Question: Solve for $a$, $ -\dfrac{5a + 5}{20a - 12} = -\dfrac{1}{20a - 12} - \dfrac{6}{10a - 6} $
Solution: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $20a - 12$ $20a - 12$ and $10a - 6$ The common denominator is $20a - 12$ The denominator of the first term is already $20a - 12$ , so we don't need to change it. The denominator of the second term is already $20a - 12$ , so we don't need to change it. To get $20a - 12$ in the denominator of the third term, multiply it by $\frac{2}{2}$ $ -\dfrac{6}{10a - 6} \times \dfrac{2}{2} = -\dfrac{12}{20a - 12} $ This give us: $ -\dfrac{5a + 5}{20a - 12} = -\dfrac{1}{20a - 12} - \dfrac{12}{20a - 12} $ If we multiply both sides of the equation by $20a - 12$ , we get: $ -5a - 5 = -1 - 12$ $ -5a - 5 = -13$ $ -5a = -8 $ $ a = \dfrac{8}{5}$